Question

1. a car comes to a stop, taking 10 m to do so with a braking force of 7500 n. calculate the work done by the brakes. make sure to draw the vectors force and displacement. givens: f = ____ s = __ unknowns: what are you solving for? ____ equation to use: substitute & solve:

Explanation:

Step1: List given values

$F = 7500\ \text{N}$, $s = 10\ \text{m}$, angle $\theta = 180^\circ$ (force opposes displacement)

Step2: Recall work formula

$W = F s \cos\theta$

Step3: Substitute values

$W = 7500 \times 10 \times \cos(180^\circ)$

Step4: Calculate final value

$\cos(180^\circ) = -1$, so $W = 7500 \times 10 \times (-1) = -75000\ \text{J}$

Vector Diagram Description:

• Draw a horizontal arrow pointing right to represent displacement vector $\vec{s}$ (length proportional to 10 m).
• Draw a horizontal arrow pointing left (opposite direction) starting from the same point to represent braking force vector $\vec{F}$ (length proportional to 7500 N).

Answer:

The work done by the brakes is $\boldsymbol{-75000\ \text{J}}$.
Givens:
$F = 7500\ \text{N}$
$s = 10\ \text{m}$
Unknowns:
What are you solving for? Work done ($W$)
Equation to use: $W = F s \cos\theta$
Substitute & Solve: $W = 7500 \times 10 \times \cos(180^\circ) = -75000\ \text{J}$